Which of the following is the third term of the expansion (a + b) n ?
C(n, 2)a^(n-2) - b^2
C(n, 3)a^(n-3) - b
C(n, 2)a^2 - b^(n - 2)

your calculations for volume (pi x r^2 × h) and surface area (2 × pi × r (h+r)) are correct. However your ratio are incorrect. From the formulas the ratio of surface area to volume would be r×h:2(h+r)

Answer:

[tex]6\sqrt{2}[/tex]

Step-by-step explanation:

we have

[tex]3\sqrt{24} -2\sqrt{54}+2\sqrt{18}[/tex]

we know that

[tex]\sqrt{24}=\sqrt{2^{3}3}=2\sqrt{6}[/tex]

[tex]\sqrt{54}=\sqrt{3^{3}2}=3\sqrt{6}[/tex]

[tex]\sqrt{18}=\sqrt{3^{2}2}=3\sqrt{2}[/tex]

Substitute

[tex]3(2\sqrt{6}) -2(3\sqrt{6})+2(3\sqrt{2})[/tex]

[tex](6\sqrt{6}) -(6\sqrt{6})+(6\sqrt{2})[/tex]

[tex]6\sqrt{2}[/tex]

When simplifying the square roots in the expression 3sqrt(24) - 2sqrt(54) + 2sqrt(18), we find that the simplified solution is 6sqrt(2).

To simplify the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18, we first need to break down each square root into its simplest form. In order to do this, we look for perfect-square factors (numbers like 4, 9, 16, 25 that have an integer as a square root) within each number:

3sqrt(24) = 3sqrt(4*6) = 6sqrt(6)

2sqrt(54) = 2sqrt(9*6) = 6sqrt(6)

2sqrt(18) = 2sqrt(9*2) = 6sqrt(2)

Because the sqrt(6) terms are like terms we can combine those, and then include the sqrt(2) term:

6sqrt(6) - 6sqrt(6) + 6sqrt(2) = 6sqrt(2).

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We know that perimeter of the triangle its a+b+c=25

a=2b-2

b=b

c=b+3

Now we can substitute it into the formula

2b-2+b+b+3=25

4b+1=25          /-1

4b=24             /:4

b=6 - its b side

a=2*6-2

a=12-2=10 - its a side

c=6+3=9 - its c side

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Answer: 169

Step-by-step explanation:

You just multiply 13 by 13

When simplifying 13 to the power of 2, you multiply 13 by itself, resulting in 13 x 13, which equals 169. This is known as squaring a number.

The question you've asked involves exponents, which is a way to express repeated multiplication of the same number. When you write 13 with a tiny 2 next to it, you're indicating that 13 should be multiplied by itself once, which is what squaring a number means. In other words, 13 to the power of 2 is 132, which is 13 × 13.

Let's simplify 132:

So, 132 equals 169. This process is using an integer power, which involves multiplying the base (in this case, 13) by itself as many times as indicated by the exponent (in this case, 2). This can apply to any number, where for example 53 (5 cubed) equals 5 × 5 × 5, which is 125.

Answer:

The answer is 1.4 miles ⇒ answer (d)

Step-by-step explanation:

* Let the balloon is at the vertex A, and the soccer fields

  at vertex B and the football field at vertex C

∴ m∠B = 20° 15' = 20.25°

∴ m∠C = 62° 30' = 62.5°

∴ m∠A = 180 - 20.25 - 62.5 = 97.25°

∵ BC = 4 miles

* By using the sin Rule:

∵ AC/sin(B) = BC/sin(A)

∴ AC = (BC)(sinB)/sin(A)

∴ AC = [4 × sin(20.25)] ÷ sin(97.25) = 1.395 ≅ 1.4 miles

∴ The distance from the balloon to the football filed = 1.4 miles

Answer:

1.4

Step-by-step explanation:

The sum of any negative number and its opposite is 0. So your answer is 0.

The sum of any negative number and its opposite is equal to 0.

Answer:

The answer is C. 9^-2

Step-by-step explanation:

Don’t know but not the first one

[tex] \tan(60°) = \frac{x}{OR} \\ \Leftrightarrow x = OR \tan(60°) = OP \sqrt{3} = 12 \sqrt{3} [/tex]

Answer:

For the Critical Reading part: P = 0.6578

For the Math part: P = 0.6578

Step-by-step explanation:

See attached photo for solutions

The probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population means of 502 (Critical Reading) and 515 (Mathematics) on the SAT is approximately 68.26% for both.

To calculate the probability for each section of the SAT, we use the formula for the z score: z = (X - μ) / (σ / sqrt(n)). In this case, X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

For the Critical Reading section, μ = 502, X is between 492 and 512 (502 ±10), σ = 100, and n = 90. When we input these values into the formula, we get a z value of -1 (for 492) and 1 (for 512) approximately. We then use a z-table to find the probability associated with these z-values. The probability for z = -1 is 0.1587 and for z = 1 is 0.8413. To find the probability that the sample mean lies within these z values, we subtract the lower probability from the higher one, which gives us 0.6826 or 68.26%.

The same steps are applied to the Mathematics section where μ = 515. The resulting probability also comes to around 68.26% that a sample mean test score will be within 10 points of the population mean.

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Answer: 26.24

32% of 82

0.32 • 82 = 26.24

Diameter is the distance all the way across a circle (going through the center), and radius is the distance from the center to the edge. This means that the radius is always half of the diameter. If the diameter is 24, the radius is 24/2 = 12 inches.

Answer:

12

Step-by-step explanation:

it would be half of 24 which is half of the wheel

Answer:

[tex]y=\frac{1}{3}x+2[/tex]

Step-by-step explanation:

The given system of equation is;

[tex]x-3y=-6...(1)[/tex]

and

[tex]2x-7y=10...(2)[/tex]

To solve for y in the first equation; we add [tex]-x[/tex] to both sides.

[tex]-3y=-6-x[/tex]

We now divide through by -3;

This implies that;

[tex]y=\frac{1}{3}x+2[/tex]

Answer:

  3x + 3y = 9

Step-by-step explanation:

Multiplying the given equation by 3 gives you ...

  3(x + y) = 3(3)

  3x + 3y = 9 . . . . . . matches the last choice

This is an equation for the same line as the given equation, so the lines will have infinitely many points in common (infinitely many solutions).

Answer:

3x + 3y = 9

Step-by-step explanation:

Answer:

  5

Step-by-step explanation:

The integers 5 and 5 sum to 10 and have the largest possible product.

___

The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.

If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.

Answer:

D

Step-by-step explanation:

Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost. The expression f(x) ∘ g(x) means f(g(x)).

Let f(x) = x(2 - x) and g(x) = 3^x.

Begin by substituting g(x) in for x in f(x).

[tex]f(g(x)) = (3^x)(2-(3^x))[/tex]

The solution is D.

D

The time worked is directly proportional to the wages. This means as the wages increase, the hours of work increases.

Answer:

the answer is A, 3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Stem Leaf Plot : A special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

So, In the Given Stem leaf plot the numbers are :

100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49

Arrange in ascending order

49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101

Now we are supposed to find how many data points would be contained in the bar from 95-105

49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101

So, we can see there are 3 data points are contained in bar from 95 -105.

Hence 3 data points are contained in bar from 95 -105.

Wendy can ride 17.5 miles in 2.5 hours

Answer:

17.5 miles

Step-by-step explanation:

[tex]\frac{miles}{min} = \frac{miles}{min} \\\\\\[/tex]

Convert hours to minutes

60 minutes = 1 hour

[tex]2.5*60=150[/tex]

2.5 hours = 150 minutes

[tex]\frac{0.7}{6} = \frac{x}{150} \\\\\\[/tex]

Cross multiply

[tex]0.7*150=6*x\\105=6x\\\frac{105}{6} =x\\17.5=x[/tex]

Answer:

x < 5

Step-by-step explanation:

Any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be LESS than 5 only.

Answer:

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

We assume that the die and coins are non-bias.

If you roll a die once, you have 6 possible outcomes (anything from 1-6).

If you flip 3 coins once, you have 2 possible outcomes for each coin (either heads or tails). Multiply those 3 possibilities (2x2x2), you get 8.

Multiply 8 with 6, and you get 48 possible outcomes in sample space.

*In the sample space shown below, do the same combinations to all roll die outcomes to get the whole sample space (i.e., 2TTT, 3TTT, 4TTT etc.).

Answer:

It is B. hyperbola, 45 degrees.

SteIt is p-by-step explanation:

If we rotate the standard form  x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.

xy = -2.5 comes from x^2 - y^2 = -5  being rotated 45 degrees.

Answer:

The correct option is b

Step-by-step explanation:

The given equation is

[tex]xy=-2.5[/tex]

It can be written as

[tex]xy+2.5=0[/tex]              .... (1)

The general forms of conic is

[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]             .... (2)

From (1) and (2), we get

[tex]A=0,B=1,C=0,D=0,E=0,E=2.5[/tex]

[tex]B^2-4AC=1-4(0)(0)=1>0[/tex]

Since the value of B²- 4AC > 0, then it is hyperbola.

The formula form angle of rotation is

[tex]\tan 2\theta=\frac{B}{A-C}[/tex]

[tex]\tan 2\theta=\frac{1}{0-0}[/tex]

[tex]\tan 2\theta=\infty[/tex]

[tex]\tan 2\theta=\tan (90^{\circ})[/tex]

[tex]2\theta=90^{\circ}[/tex]

[tex]\theta=45^{\circ}[/tex]

The angle of rotation is 45°. Therefore the correct option is b.

Answer:

192

Step-by-step explanation:

To find how many phones are expected to be defective, we need to represent the values in a fraction.

[tex]\dfrac{x}{8000}=\dfrac{3}{125}[/tex]

x = number of defective phones

Now we can solve this using algebra.

To get the value of x we need to multiply both sides by 8000 to leave x alone.

[tex]x=\dfrac{3}{125}(8000)[/tex]

[tex]x=0.024(8000)[/tex]

[tex]x=192[/tex]

So around 192 cell phones are expected to be defective out of 8000 phones.

Answer:

192

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

The normal distribution describes how the values of a variable are distributed. Given a mean of 15 and standard deviation of 5.95, the area within which values lie could be found using the properties of a normal distribution, which state that ~68% of data falls within one standard deviation of the mean, ~95% within two standard deviations, and ~99.7% within three standard deviations.

This question is related to the normal distribution in statistics. The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.

Given a normal distribution with a mean of 15 and a standard deviation of 5.95, we are asked to find the area within which the values lie. Using the properties of a normal distribution, we know that:

So, if we wanted to find the area within one standard deviation of the mean, for instance, we would calculate the values of (mean - standard deviation) and (mean + standard deviation), which would represent the range within which approximately 68% of the data lies.

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The amount that need to be pay is $250.

= 4% of 4,200 + $47 + $35

= $168 + $47 + $35

= $250

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Samantha needs to pay a total of $250 in extra charges, which includes $168 for the state tax, $47 for the license plate, and $35 for the state safety and emission inspection.

To determine how much Samantha needs to pay in extra charges for her automobile purchase, we need to calculate each component separately and then sum them up. Firstly, we calculate the state tax by multiplying the purchase price by the tax percentage:

Tax = Purchase Price × Tax Rate

Tax = $4,200 × 0.04 = $168

Next, we add the fixed costs for the license plate and state safety and emission inspection:

Total Extra Charges = Tax + License Plate Fee + Inspection Fee

Total Extra Charges = $168 + $47 + $35 = $250

Therefore, Samantha needs to pay $250 in extra charges, not including the price of the car.

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Answer:

The possible solution that is obtained from the system of equation are:

(1,3) and (6,13)

Step-by-step explanation:

We are asked to find the solution set of the given system of equation as:

[tex]y=x^2-5x+7-----------(1)[/tex]

and [tex]y=2x+1--------(2)[/tex]

We know that the solution of the system of equations is the possible set of x and y-values that satisfy both the equations.

Or we may say the point of intersection of the graph that is obtained from both the equations.

We solve the system by substitution method as:

We put the value of y from equation (1) in equation (2) to obtain:

[tex]x^2-5x+7=2x+1[/tex]

which is further written by combining the like terms as:

[tex]x^2-5x-2x+7-1=0\\\\x^2-7x+6=0\\\\x^2-6x-x+6=0\\\\x(x-6)-1(x-6)\\\\(x-1)(x-6)=0[/tex]

Hence, we get the possible values of x as:

x=1   and x=6

   y=2×1+1=2+1  ( Putting the value of x in equation (2))

         y=3

          y=2×6+1

             y=13

Hence, the possible solutions are:

(1,3) and (6,13)

Answer:

Step-by-step explanation:

Draw a generic normal curve.  Subdivide the x-axis on each side of the center (mean) into four approx. = parts.

Label the mean with '50.'

1 std. dev. below the mean would be 50-2 = 48;

2 std. dev.                             would be 48-2= 46, and

3 std dev.                               would be 46 - 2 = 44

Do the same on the other side of the mean.  

The 3 corresponding values will be 52, 54 and 56.

Answer:

[tex]w=V/(lh)[/tex]

Step-by-step explanation:

Let

l------> the length of the base of the prism

w------> the width of the base of the prism

h------> the height of the prism

we know that

The volume of the prism is equal to

[tex]V=lwh[/tex]

Solve for w

That means-------> isolate the variable w

so

Divide both sides by (lh)

[tex]V/(lh)=lwh/(lh)[/tex]

Simplify

[tex]w=V/(lh)[/tex]

The sum of two numbers is 60

The answer is

40 and 20

Answer:

The length of 30 inches is longer

Step-by-step explanation:

we know that

[tex]1\ ft=12\ in[/tex]

Convert the length to inches

[tex]2\ ft=2(12)=24\ in[/tex]

therefore

[tex]30\ in>24\ in[/tex] ------> [tex]30\ in>2\ ft[/tex]

The length of 30 inches is longer